Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened. A. forall x [(Tiger(x) ^ Lion(x)) -> ((hungry(x) v threatened(x)) -> attack(x))] B. forall x [(Tiger(x) v Lion(x)) -> ((hungry(x) ^ threatened(x)) -> attack(x))] C. forall x [(Tiger(x) ^ Lion(x)) ^ (hungry(x) v threatened(x)) -> attack(x)] D. forall x [(Tiger(x) v Lion(x)) ^ (hungry(x) v threatened(x)) -> attack(x)]

GATE 2006 · Discrete Mathematics · First Order Logic · medium

Answer: D. forall x [(Tiger(x) v Lion(x)) ^ (hungry(x) v threatened(x)) -> attack(x)]

1. Parse the subject: 'tigers and lions': The subject 'tigers and lions' means any individual that is a Tiger OR a Lion. So the species condition is Tiger(x) v Lion(x).
2. Parse the condition: 'if hungry or threatened': The trigger 'if hungry or threatened' gives the disjunction hungry(x) v threatened(x). Either alone suffices.
3. Combine into final formula: Full formula: forall x [(Tiger(x) v Lion(x)) ^ (hungry(x) v threatened(x)) -> attack(x)]. This is option D.